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Two types of vehicle use the university central bus station: Uni-link buses and National Express coaches.
a) On average, a National Express coach arrives every two hours. What is the probability that only one bus will arrive in a four hour period?
b) On the U1 Uni-link bus route, buses either go to the airport or to the docks. Other Uni-link routes do not go to the airport. At the bus station, half of the U1 buses which arrive are going to the airport. At midday, 10% of the Uni-link buses are full. Of these particular buses, 30% are airport buses on the U1 route. U1 buses make up 40% of the Uni-link arrivals at the bus station. What is the probability that a bus is full at midday, given that it is an Airport U1 bus?
c) Are the events ‘bus is full' and ‘bus is going to the Airport' independent? Show your reasoning.
d) On average, a certain number, k, of National Express coaches go to Bournemouth every day. It is found that the probability of n coaches going to Bournemouth in a day is e-k What is n?
Use the hypergeometric formula to find this probability. The lottery commission also pays if a contestant matches 4 or 5 of the 6 winning numbers. Hint: Divide the 44 numbers into two groups, winning numbers and nonwinning numbers.
The objective function always includes all of the decision variables, but that is not necessarily true of the constraints. Explain the difference between the objective function and the constraints. Then, explain why a constraint need not refer to all..
Compute 99% confidence intervals for the average daily maximum temperature in August for each of the three years in which you collected data. How do they compare?
While the 46 afternoon students' average score was 79.44 with a standard deviation of 6.62. (a) Which test would you use to compare the means?
Analyze these data and summarize your findings for managers. Explain how information can be used by decision makers. Assume that sales per customer are normally distributed.
For each of the following, indicate whether or not you would expect it to have a strong seasonal component and why.
Determine the probability that a randomly selected exam will have a score of at least 71? What percentage of exams will have scores between 89 and 92?
A health services provider has been reimbursed by a national health insurance organization for a large number of services. It appears that overpayments may have occurred on many of the reimbursements
Complete the table and answer the following questions. Use the .05 significance level.
If we wish to be 95% certain of avoiding a Type I error, use these data to examine differences in the average distance traveled to the two clinics.
The lowess fitted value is 0.883. Thus the value of adj discussed on the previous slide is 0.883 for spots with A=7. How is the lowess curve determined?
Weight of the .5 cubic yard bag of landscape much is normally distributed with mean of 40 pounds and standard deviation of 1. Determine the probability that the bag will weigh more than 40 pounds?
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